I had once the same problem with my portable keg-o. Not was bad as on your picture, but enough... I ended up dumping the co2 line since I first didn't notice and then couldn't clean it out anymore. Not sure how I managed to do that since it had never happened before and never after but it is a mess!
Don't know how to clean a regulator (if that's even possible) but rins your lines and let them dry. Possibly blow the lines to get the water out to dry faster.

The lines went straight into the trash bin. I'm really only concerned about the regulator. Beer came out of the hole on the side of the regulator screw, so I know it's a mess in there. I'm so angry. I wouldn't have bought these valves if I didn't believe they were check valves, but the description on the website doesn't say they are. I don't know what happened.

That's what I was hoping, but I can't figure out how to get this unit apart :/ The main knob doesn't unscrew all the way - I can see a circlip at the bottom of it. There are no other screws on the body of the regulator.